Beam support reactions worksheet with answers

Free printable Beam support reactions worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
P = 15 kN, 30°ABRA​ = ?1 m4 m

The simply supported beam has a pin at A and a roller at B. A point load P acts at 1 m from A, inclined at 30° to the horizontal. Find the vertical support reaction RA.

L = 5 mP = 15 kN at 1 mθ = 30°
RA = kN
2.Easy
P = 45 kNABRA​RB​ = ?2.5 m2.5 m

The simply supported beam has a pin at A and a roller at B. Find the vertical support reaction RB.

L = 5 mP = 45 kN at 2.5 m
RB = kN
3.Medium
w0​ = 12 kN/mABRB​ = ?6 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that rises from zero at A to 12 kN/m at B. Find the vertical support reaction RB.

L = 6 mw0 = 12 kN/m
RB = kN
4.Medium
w = 12 kN/mP = 65 kNABRA​ = ?1.5 m0.5 m2 m

The cantilever beam is fixed to the wall at A. It carries a uniformly distributed load w from the wall to 2 m and a point load P at 1.5 m from the wall. Find the vertical reaction RA at the wall.

L = 4 mP = 65 kN at 1.5 mw = 12 kN/m from 0 to 2 m
RA = kN
5.Hard
w = 3 kN/mP = 55 kNABRA​ = ?RB​2 m5 m1 m

The simply supported beam has a pin at A and a roller at B. Find the vertical support reaction RA.

L = 8 mP = 55 kN at 7 mw = 3 kN/m from 2 to 7 m
RA = kN
6.Hard
w0​ = 15 kN/mP = 40 kNABMA​ = ?4 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is 15 kN/m at the wall and falls to zero at the free end B, plus a point load P at 4 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 4 mw0 = 15 kN/mP = 40 kN at 4 m
MA = kN·m

Answer key

  1. 1. RA = 6 kN
  2. 2. RB = 22.5 kN
  3. 3. RB = 24 kN
  4. 4. RA = 89 kN
  5. 5. RA = 13.44 kN
  6. 6. MA = 200 kN·m

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